Problem: Solve for $x$ and $y$ using elimination. ${-5x-3y = -39}$ ${-6x+3y = 6}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-11x = -33$ $\dfrac{-11x}{{-11}} = \dfrac{-33}{{-11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-5x-3y = -39}\thinspace$ to find $y$ ${-5}{(3)}{ - 3y = -39}$ $-15-3y = -39$ $-15{+15} - 3y = -39{+15}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {-6x+3y = 6}\thinspace$ and get the same answer for $y$ : ${-6}{(3)}{ + 3y = 6}$ ${y = 8}$